Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Top down and bottom up engineering of bone

The goal of this retrospective article is to place the body of my lab's multiscale mechanobiology work in context of top-down and bottom-up engineering of bone. We have used biosystems engineering, computational modeling and novel experimental approaches to understand bone physiology, in health and disease, and across time (in utero, postnatal growth, maturity, aging and death, as well as evolution) and length scales (a single bone like a femur, m; a sample of bone tissue, mm-cm; a cell and its local environment, μm; down to the length scale of the cell's own skeleton, the cytoskeleton, nm). First we introduce the concept of flow in bone and the three calibers of porosity through which fluid flows. Then we describe, in the context of organ-tissue, tissue-cell and cell-molecule length scales, both multiscale computational models and experimental methods to predict flow in bone and to understand the flow of fluid as a means to deliver chemical and mechanical cues in bone. Addressing a number of studies in the context of multiple length and time scales, the importance of appropriate boundary conditions, site specific material parameters, permeability measures and even micro-nanoanatomically correct geometries are discussed in context of model predictions and their value for understanding multiscale mechanobiology of bone. Insights from these multiscale computational modeling and experimental methods are providing us with a means to predict, engineer and manufacture bone tissue in the laboratory and in the human body.     

Determination of the number of water molecules in the proton pathway of bacteriorhodopsin using neutron diffraction data

It has been shown that water molecules participate in the proton pathway of bacteriorhodopsin. Large efforts have been made to determine with various biophysical methods the number of water molecules involved. Neutron diffraction H2O/D2O exchange experiments have been often used to reveal the position of water even with low-resolution diffraction data. With this technique, care must be taken with the limitations of the difference Fourier method which are commonly applied to analyze the data. In this paper we compare the results of the difference Fourier method applied to measured diffraction data (not presented here) and models with those from alternative methods introduced here: (1) a computer model calculation procedure to determine a label's scattering length density based on a comparison of intensity differences derived from models and intensity differences from our measurements; (2) a method based on the Parseval formula. Both alternative methods have been evaluated and tested using results of neutron diffraction experiments on purple membranes (Hauss et al. 1994). Our findings indicate that the difference Fourier method applied to low-resolution diffraction data can successfully determine the position of localized water molecules but underestimates their integrated scattering length density in the presence of labels in other positions. Furthermore, we present the results of neutron diffraction experiments on purple membranes performed to determine the number of water molecules in the projected area of the Schiff base at 86%, 75% and 57% relative humidity (r.h.). We found 19 +/- 2 exchangeable protons at 75% r.h., which means at least 8-9 water molecules are indispensable for normal pump function.     

Use of structure comparison methods for the refinement of protein structure predictions. I. Identifying the structural family of a protein from low-resolution models.

Predicting the three-dimensional structure of proteins is still one of the most challenging problems in molecular biology. Despite its difficulty, several investigators have started to produce consistently low-resolution predictions for small proteins. However, in most of these cases, the prediction accuracy is still too low to make them useful. In the present article, we address the problem of obtaining better-quality predictions, starting from low-resolution models. To this end, we have devised a new procedure that uses these models, together with structure comparison methods, to identify the structural family of the target protein. This would allow, in a second step not described in the present work, to refine the predictions using conserved features of the identified family. In our approach, the structure database is investigated using predictions, at different accuracy levels, for a given protein. As query structures, we used both low-resolution versions of the native structures, as well as different sets of low accuracy predictions. In general, we found that for predictions with a resolution of > or =5-7 A, structure comparison methods were able to identify the fold of a protein in the top positions.     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.     

Multiscale simulations of protein and membrane systems

Classical multiscale simulations are perfectly suited to investigate biological soft matter systems. Owing to the bridging between microscopically realistic and lower-resolution models or the integration of a hierarchy of subsystems, one gets access to biologically relevant system sizes and timescales. In recent years, increasingly complex systems and processes have come into focus such as multidomain proteins, phase separation processes in biopolymer solutions, multicomponent biomembranes, or multiprotein complexes up to entire viruses. The review shows factors that have contributed to this progress — from improved models to machine-learning-based analysis and scale-bridging methods.     

Multiscale model for pulmonary oxygen uptake and its application to quantify hypoxemia in hepatopulmonary syndrome

This paper presents a novel multiscale methodology for quantitative analysis of pulmonary gas exchange. The process of oxygen uptake in the lungs is a complex multiscale process, characterized by multiple time and length scales which are coupled nonlinearly through the processes of diffusion, convection and reaction, and the overall oxygen uptake is significantly influenced by the transport and reaction rate processes at the small-scales. Based on the separation of length scales, we characterize these disparate scales by three representative ones, namely micro (red blood cell), meso (capillary and alveolus) and macro (lung). We start with the fundamental convection-diffusion-reaction (CDR) equation that quantifies transport and reaction rates at each scale and apply spatial averaging techniques to reduce the dimensionality of these models. The resultant low-dimensional models embed each scale hierarchically within the other while retaining the important parameters of the small-scales in the averaged equations, and drastically reduce the computational efforts involved in solving them. We use our multiscale model for pulmonary gas exchange to quantify the oxygen uptake abnormalities in patients with hepatopulmonary syndrome (HPS), a disease which is characterized by coupled abnormalities in multiple length scales. Based on our multiscale modeling, we suggest a strategy to stratify patients with HPS into two categories--those who are oxygen-responsive and those who are oxygen non-responsive with intractable hypoxemia.     

Enzyme closure and nucleotide binding structurally lock guanylate kinase

We investigate the conformational dynamics and mechanical properties of guanylate kinase (GK) using a multiscale approach combining high-resolution atomistic molecular dynamics and low-resolution Brownian dynamics simulations. The GK enzyme is subject to large conformational changes, leading from an open to a closed form, which are further influenced by the presence of nucleotides. As suggested by recent work on simple coarse-grained models of apo-GK, we primarily focus on GK's closure mechanism with the aim to establish a detailed picture of the hierarchy and chronology of structural events essential for the enzymatic reaction. We have investigated open-versus-closed, apo-versus-holo, and substrate-versus-product-loaded forms of the GK enzyme. Bound ligands significantly modulate the mechanical and dynamical properties of GK and rigidity profiles of open and closed states hint at functionally important differences. Our data emphasizes the role of magnesium, highlights a water channel permitting active site hydration, and reveals a structural lock that stabilizes the closed form of the enzyme.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.     

Shaker pore structure as predicted by annealed atomic simulation using symmetry and novel geometric restraints

Recent studies making use of channel-blocking peptides as molecular calipers have revealed the architecture of the pore-forming region of Shaker-type potassium channels. Here we show that the low-resolution, experimentally derived geometric information can be incorporated as restraints within the context of an annealed molecular dynamics simulation to predict an atomic structure for the channel pore which, by virtue of restraints, conforms to the experimental evidence. The simulation is reminiscent of the computational method employed by nuclear magnetic resonance (NMR) spectroscopists to resolve solution structures of biological macromolecules, but in lieu of restraints conventionally derived from NMR spectra, novel restraints are developed that include side-chain orientation of amino acid residues and assumed symmetry of protein subunits. The method presented here offers the possibility of expanding cooperation between simulation and experiment in developing structural models, especially for systems such as ion channels whose three-dimensional structures may not be amenable to determination by direct methods at the present time.     

Biased coarse-grained molecular dynamics simulation approach for flexible fitting of X-ray structure into cryo electron microscopy maps

Several approaches have been introduced to interpret, in terms of high-resolution structure, low-resolution structural data as obtained from cryo-EM. As conformational changes are often observed in biological molecules, these techniques need to take into account the flexibility of proteins. Flexibility has been described in terms of movement between rigid domains and between rigid secondary structure elements, which present some limitations for studying dynamical properties. Normal mode analysis has also been used, but is limited to medium resolution data. All-atom molecular dynamics fitting techniques are more appropriate to fit structures into higher-resolution data as full protein flexibility is considered, but are cumbersome in terms of computational time. Here, we introduce a coarse-grained approach; a Go-model was used to represent biological molecules, combined with biased molecular dynamics to reproduce accurately conformational transitions. Illustrative examples on simulated data are shown. Accurate fittings can be obtained for resolution ranging from 5 to 20 Å. The approach was also tested on experimental data of Elongation Factor G and Escherichia coli RNA polymerase, where its validity is compared to previous models obtained from different techniques. This comparison demonstrates that quantitative flexible techniques, as opposed to manual docking, need to be considered to interpret low-resolution data.     

Prediction of protein oligomer structures using GALAXY in CASP13

Many proteins need to form oligomers to be functional, so oligomer structures provide important clues to biological roles of proteins. Prediction of oligomer structures therefore can be a useful tool in the absence of experimentally resolved structures. In this article, we describe the server and human methods that we used to predict oligomer structures in the CASP13 experiment. Performances of the methods on the 42 CASP13 oligomer targets consisting of 30 homo-oligomers and 12 hetero-oligomers are discussed. Our server method, Seok-assembly, generated models with interface contact similarity measure greater than 0.2 as model 1 for 11 homo-oligomer targets when proper templates existed in the database. Model refinement methods such as loop modeling and molecular dynamics (MD)-based overall refinement failed to improve model qualities when target proteins have domains not covered by templates or when chains have very small interfaces. In human predictions, additional experimental data such as low-resolution electron microscopy (EM) map were utilized. EM data could assist oligomer structure prediction by providing a global shape of the complex structure.     

Matching theory and experiment in protein folding.

There has been considerable progress made over the past year in linking experimental and theoretical approaches to protein folding. Recent results from several independent lines of investigation suggest that protein folding mechanisms and landscapes are largely determined by the topology of the native state and are relatively insensitive to details of the interatomic interactions. This dependence on low-resolution structural features, rather than high-resolution detail, suggests that it should be possible to describe the fundamental physics of the folding process using relatively low-resolution models. Recent experiments have set benchmarks for testing new models and progress has been made in developing theoretical models for interpreting and predicting experimental results.     

Characteristic length scales of spatial models in ecology via fluctuation analysis

A technique of fluctuation analysis is introduced for the identification of characteristic length scales in spatial models, with similarities to the recently introduced methods using correlations. The identified length scale provides the optimal size to extract non-trivial large-scale behaviour in such models. The method is demonstrated for three biological models: genetic selection, plant competition and a complex marine system; the first two are coupled map lattices and the last one is a cellular automaton. These cover the three possibilities for asymptotic (long time) dynamics: fixation (the system converges to a fixed point); statistical fixation (the spatial statistics converge to fixed values); and complex statistical structure (the statistics do not converge to fixed values). The technique is shown to have an additional use in the identification of aggregation or dispersal at various scales. The method is rigorously justifiable in the cases when the system under analysis satisfies the FKG (Fortuin-Kasteleyn-Ginibre) property and has a fast decay of correlations. We also discuss the connection between the fluctuation analysis length scale and hydrodynamic limits methods to derive large scale equations for ecological models. <br>     

Adaptive multiscale principal component analysis for on-line monitoring of a sequencing batch reactor

In recent years, multiscale monitoring approaches, which combine principal component analysis (PCA) and multi-resolution analysis (MRA), have received considerable attention. These approaches are potentially very efficient for detecting and analyzing diverse ranges of faults and disturbances in chemical and biochemical processes. In this work, multiscale PCA is proposed for fault detection and diagnosis of batch processes. Using MRA, measurement data are decomposed into approximation and details at different scales. Adaptive multiway PCA (MPCA) models are developed to update the covariance structure at each scale to deal with changing process conditions. Process monitoring by a unifying adaptive multiscale MPCA involves combining only those scales where significant disturbances are detected. This multiscale approach facilitates diagnosis of the detected fault as it hints to the time-scale under which the fault affects the process. The proposed adaptive multiscale method is successfully applied to a pilot-scale sequencing batch reactor for biological wastewater treatment.     

Multiscale Analysis of Biological Systems

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.     

Biological clocks as age estimation markers in animals: a systematic review and meta-analysis

Various biological attributes associated with individual fitness in animals change predictably over the lifespan of an organism. Therefore, the study of animal ecology and the work of conservationists frequently relies upon the ability to assign animals to functionally relevant age classes to model population fitness. Several approaches have been applied to determining individual age and, while these methods have proved useful, they are not without limitations and often lack standardisation or are only applicable to specific species. For these reasons, scientists have explored the potential use of biological clocks towards creating a universal age-determination method. Two biological clocks, tooth layer annulation and otolith layering have found universal appeal. Both methods are highly invasive and most appropriate for post-mortem age-at-death estimation. More recently, attributes of cellular ageing previously explored in humans have been adapted to studying ageing in animals for the use of less-invasive molecular methods for determining age. Here, we review two such methods, assessment of methylation and telomere length, describing (i) what they are, (ii) how they change with age, and providing (iii) a summary and meta-analysis of studies that have explored their utility in animal age determination. We found that both attributes have been studied across multiple vertebrate classes, however, telomere studies were used before methylation studies and telomere length has been modelled in nearly twice as many studies. Telomere length studies included in the review often related changes to stress responses and illustrated that telomere length is sensitive to environmental and social stressors and, in the absence of repair mechanisms such as telomerase or alternative lengthening modes, lacks the ability to recover. Methylation studies, however, while also detecting sensitivity to stressors and toxins, illustrated the ability to recover from such stresses after a period of accelerated ageing, likely due to constitutive expression or reactivation of repair enzymes such as DNA methyl transferases. We also found that both studied attributes have parentally heritable features, but the mode of inheritance differs among taxa and may relate to heterogamy. Our meta-analysis included more than 40 species in common for methylation and telomere length, although both analyses included at least 60 age-estimation models. We found that methylation outperforms telomere length in terms of predictive power evidenced from effect sizes (more than double that observed for telomeres) and smaller prediction intervals. Both methods produced age correlation models using similar sample sizes and were able to classify individuals into young, middle, or old age classes with high accuracy. Our review and meta-analysis illustrate that both methods are well suited to studying age in animals and do not suffer significantly from variation due to differences in the lifespan of the species, genome size, karyotype, or tissue type but rather that quantitative method, patterns of inheritance, and environmental factors should be the main considerations. Thus, provided that complex factors affecting the measured trait can be accounted for, both methylation and telomere length are promising targets to develop as biomarkers for age determination in animals.     

Multiscale Systems Analysis of Root Growth and Development: Modeling Beyond the Network and Cellular Scales

Over recent decades, we have gained detailed knowledge of many processes involved in root growth and development. However, with this knowledge come increasing complexity and an increasing need for mechanistic modeling to understand how those individual processes interact. One major challenge is in relating genotypes to phenotypes, requiring us to move beyond the network and cellular scales, to use multiscale modeling to predict emergent dynamics at the tissue and organ levels. In this review, we highlight recent developments in multiscale modeling, illustrating how these are generating new mechanistic insights into the regulation of root growth and development. We consider how these models are motivating new biological data analysis and explore directions for future research. This modeling progress will be crucial as we move from a qualitative to an increasingly quantitative understanding of root biology, generating predictive tools that accelerate the development of improved crop varieties.